Temperature-induced torque noise is a fundamental limitation for precision torsion pendulums and spaceborne inertial sensors (e.g., LISA, Taiji, and TianQin) in the millihertz (mHz) band. Direct time-domain finite-element simulations can be computationally demanding for ultra-low-frequency thermal propagation and do not directly provide compact frequency-domain transfer functions. In this work, we propose a comprehensive lumped-parameter thermal network model to perform full-link frequency-domain analysis of a precision torsion pendulum. We calculate the frequency-dependent spatial thermal response and find that the increase in the temperature-to-torque response near $10mHz$ is associated with spatial thermal nonuniformity. This inhomogeneity is driven by component-specific thermal lags, which produce temperature differences that drive structural thermal distortion via the support frame and the radiometer effect via test mass surface asymmetry. Furthermore, we propose targeted structural optimization strategies, including thermal strapping, support frame lightweighting, surface emissivity homogenization, and passive thermal shielding. The calculated frequency dependence is consistent with the available temperature-modulation measurements and supports the interpretation that the high-frequency response is associated primarily with spatially nonuniform thermal responses of the support structure and test-mass surfaces. The model is further used to evaluate several thermal-design strategies, whose predicted performance remains to be tested experimentally.